Algebro-Geometric Solutions of a (<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mn>2</mn> <mo>+</mo> <mn>1</mn> </math>)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

The ( 2 + 1 )-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known id="M3"> soliton associated Ablowitz-Kaup-Newell-Segur hierarchy. Then, based on finite-order expansion matrix, a hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to straighten out flows, from which algebro-geometric solutions id="M4"> proposed by means id="M5"> θ functions.